( h:7 ) 



data, we have to write everywhere, //,/■ and A'//, instead of .v and y, 

 whence 



n.hn! JT 



The scale factors // and //' can tlien be determined by pntting 



.4o.o en .4().o = 



and the two nninixed means ot the second order can be disposed 



of for tlie determination of tliese constants : 



1 1 



f^(''^) == 2^ en nJif) = ^ 



If, fnrther, wo make the axes rotate about the origin so that they 

 coincide witii the princi|)al axes of inertia, then also .4i.i has to be 

 put equal to zero and the corresponding- mean 



ft, (-i'» .v) 

 enables us to calculate the direction of the principal axes. 

 The series (30) then becomes : 



u = tr--''^!/-[Ao + A3.0U3 + AoaL^V; + Ai.2ih To ^- ^0.3^3 + 



4- AoA V4 + enz. 



where all terms except the first represent the deviations from the 

 normal exjM)nential law, the terms of odd degree being a measure 

 of the different kinds of skewness, the terms of even degree of the 

 ditferent kinds of symmetrical deviations. 



Chemistry. — "Eqidlibrin in (/uatf'mari/ si/.'itetns." By Prof. F. A. H. 



SCHREINEMAKERS. 



Let us first take the system with the components: icater, ethyl 

 alcohol, metltyl dlcohol and timmonium nitrate; we then have 

 at the ordinary temperature one solid substance and three solvents 

 which are miscible in all })r()portions so that the resulting equi- 

 libria are very simple. The ecjuilibria occurring in this system 

 at 30° have been i)ivestigated and are represented in the usual 

 manner in Fig. J ; the angular points IF, M,A and Z of the teti*a- 

 hedron indicate the components: water, methyl alcohol, ethyl alcohol 

 and the salt: ammonium nitrate. 



The curve nur situated on the side plane WAZ represents the 

 solutions consisting of water and ethyl alcohol and saturated with 

 solid salt ; the curve ivnt represents the solutions of water and 



